An Introduction to Ab initio Molecular Dynamics Simulations

Computational Molecular Science Research Team

Y. Ootani

What is Theoretical Chemistry?

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・Explain chemical observation from physical theory ・Predict the chemical property

Theoretical Chemistry

1.00 m 1.0-10 m 1.010 m

Quantum mechanics Classical mechanics

Atom, Molecule the universe

Classical mechanics and Quantum mechanics

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Quantum Mechanics

Schrödinger equation

HΨ = EΨ

Classical Mechanics Newton’s Equations of Motion

F = ma

Schrödinger equation for molecule

No analytical solution!!

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What is “Ab initio”

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HΨ = EΨ

Ab initio calculation Latin term “from the beginning”

Molecule

Born-Oppenheimer approximation

HnucΨnuc = EnucΨnuc HeleΨele = EeleΨele

Nuclei Electron

・Spectrum ・Electric energy ・Electron density

・Molecular structure ・Magnetic property ・Chemical bond etc...

Chemical property relevant for chemical property

Solve

Fix

Ab initio calculation

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・Gaussian ・Gamess ・NWChem

Ab initio quantum chemistry software

・Dirac etc...

NTChem ・Scalable algorithm ・Highly parallelized ab initio calculation

・Molpro ・Molcas ・Turbomol

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Potential energy surface

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Potential Energy Surface : PES ポテンシャルエネルギー曲面

Excited state 励起状態

Ground state 基底状態

H H

How do nucleus move?

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Reactant Product A?

Product B?

Potential energy surface

反応物

生成物

HΨ = EΨMolecule

Born-Oppenheimer approximation

HnucΨnuc = EnucΨnuc HeleΨele = EeleΨele

Nuclei Electron

Solve Solve Fix

Large computational cost

Classical approximation

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Quantum mechanics

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HΨ = EΨMolecule

Born-Oppenheimer approximation

HnucΨnuc = EnucΨnuc HeleΨele = EeleΨele

Nuclei Electron

Solve Solve F = ma Classical approximation

Classical mechanics

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Classical approximation

Ab initio Molecular Dynamics

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(Ab initio calculation)

Electron

Nuclei Force Nuclear

Coordinate

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dissociation vibration

Ab initio Molecular Dynamics

F = ma

HeleΨele = EeleΨele

Beyond the Ab initio Molecular Dynamics

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・Born-Oppenheimer approximation ・Classical approximation

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Two approximations

Efficient schemes are required to reproduce these phenomena.

・Surface Hopping −Intuitive method

・Ehrenfest

・Semi-classical method −Mathematically complex −No practical scheme

Can not reproduce

・Nonadiabatic transition ・Tunneling effect 非断熱遷移

Nonadiabatic transition

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DNA basis all-trans retinal

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11-cis retinal

Nonadiabatic transition

Photoisomerization of azabenzene

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Azobenzene

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J.Am.Chem.Soc. 128, 6284 (2006)

J.Am.Chem.Soc. 125, 9542 (2003)

J.Am.Chem.Soc. 129, 6396 (2007)

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Surface Hopping

trans cis

アゾベンゼンの光異性化

Photoisomerization of azobenzene

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cis → trans

・Isomerization occurs via rotation pathway. ・Two pathways are found.

Photoisomerization of azobenzene

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trans→ cis

・Trans-azobenzene has longer lifetime than cis-azobenzene. ・Isomerization occurs via rotation pathway.

Photoisomerization of azobenzene

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Our  results Exp.

cis  →　trans 0.45 0.4  –  0.56

trans  →  cis 0.28±0.14 0.23  –  0.25

Blanching ratio

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・Calculated blanching ratio are in good agreement with experimental results.

Computational cost

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・Ab initio calculation : 3 min ・Simulation time : 240fs ・Time step : 1.0 fs

3min × (240÷1.0) = 12h

Example

200 trajectories

Computationally demanding

(Ab initio calculation)

Electron

Nuclei Force Nuclear

Coordinate

F = ma

HeleΨele = EeleΨele

cis → trans ・Ab initio calculation : 3 min ・Simulation time : 1000 ～ 3000fs ・Time step : 1.0 fs

3min × (1000～3000÷1.0) = 50～150h 100 trajectories

trans → cis

Nuclear Quantum Effect

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Tunneling Effect

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Umbrella inversion of ammonia

Proton transfer in 7-azaindole dimer

Intramolecular hydrogen transfer in malonaldehyde

Nuclear quantum effect

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・Ab initio calculation : 3 min ・Number of atoms : 9

−21 degrees of freedom ・Number of grids : 5 ・Time step : 0.2fs ・Simulation time : 500fs

3min × 521 × (500÷0.2) ≒ 7×1012 year! !"#$%&'#()*

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・Quantum mechanical dynamics ・Semiclassical method

−Makri-Miller method −Instanton theory −Classical S-Matrix method

Computational costs of quantum mechanical dynamics

Have not been developed...

Summary

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Can computer be a test tube ?

・Solvent ・Nuclear Quantum effect

・Electron correlation ・Relativistic effect

Future work